已知3x/(x-3)(x+2)=A(x-3)-B/(x+2)是恒等式,求A,B的值

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已知3x/(x-3)(x+2)=A(x-3)-B/(x+2)是恒等式,求A,B的值
已知3x/(x-3)(x+2)=A(x-3)-B/(x+2)是恒等式,求A,B的值

已知3x/(x-3)(x+2)=A(x-3)-B/(x+2)是恒等式,求A,B的值
A(x-3)-B/(x+2)=A(x+2)/[(x-3)(x+2)]-B(x-3)/[(x-3)(x+2)]
=(Ax+2A-Bx+3B)/[(x-3)(x+2)]
=3x/[(x-3)(x+2)]
所以A-B=3 2A+3B=0
解得A=9/5 B=-6/5